NEW YORK (CNNMoney.com) — Fox Network refused Wednesday to agree to an offer by Time Warner Cable to enter arbitration with the Federal Communications Commission to resolve an ongoing fee dispute.

Fox and Time Warner Cable have been locked in a public battle over how much the cable giant should pay News Corp. for the right to deliver Fox networks into its subscribers’ homes.

Talks are still ongoing, but if a deal is not reached before the Dec. 31 deadline, all of the Fox-owned broadcast networks and some of its cable channels could disappear from some Time Warner Cable subscribers’ televisions on New Year’s Day.

The Fox statement comes after a series of letters about the dispute were made public earlier Wednesday. In its letter, Fox said it believes “these discussions do not belong in the hands of a third party” and wants to negotiate face-to-face with Time Warner Cable.

In its own letter, dated Dec. 29, Time Warner Cable said it would willingly submit to binding arbitration. That was after Sen. John Kerry, D-Mass., wrote to both Time Warner Cable and News Corp. (NWS, Fortune 500), Fox’s parent company, to urge the companies to resolve their disagreement and suggested arbitration.

Time Warner Cable also said that it would enter into an interim agreement with Fox to avoid any blackout, but Fox did not address that option on Wednesday.

A Fox Networks representative would not comment beyond what was in the letter. A Time Warner Cable spokeswoman said “we are willing to do what it takes to get the deal done, including arbitration.” She added that negotiations are ongoing “but [Fox’s] current demands are still unreasonable,” especially in during a recession.

“We are simply seeking fair compensation for content that has helped fuel the ever increasing profit margins of the cable industry,” News Corp. chief executive Chase Carey wrote in a letter to Kerry, who is the chairman of the Senate Commerce Subcommittee on Communication, Technology and the Internet.

News Corp. wants to charge Time Warner Cable (TWC) $1 per subscriber for airing its broadcast station, Fox. In the past, providers have paid a fee only for cable networks — never for broadcast television.

The contracts for six Fox cable channels — FX, Speed, Fuel TV, Fox Reality, Fox Soccer and Fox Sports en Español — as well as certain regional sports networks are also slated to expire. But Fox News Channel and Fox Business Network are not affected.

The dispute reflects television’s changing business model as programming choices continue to expand and advertising revenues plummet, noted David Wertheimer, chief executive of the Entertainment Technology Center at the University of Southern California.

Cable networks have always counted on revenue from both advertising and subscriber fees. So even as ad sales have declined, cable channels have stayed afloat on those fees, which have remained steady according to Wertheimer. But broadcast networks that rely solely on ad revenue are casting about for new sources of revenue, which is likely what’s driving Fox’s bid for higher fees.

At the same time, cable providers like Time Warner are in a costly battle to retain subscribers as they fend of threats from satellite TV and Web-based programming. Time Warner Cable argues that Fox is charging too much to renew the contract and that any cost increase would only hurt consumers.

End-of-year standoffs between cable providers and TV networks aren’t uncommon, since these deals typically expire on Dec. 31.

If the new year doesn’t bring a new agreement, it would be a lose-lose situation for the companies. Time Warner Cable’s customers would undoubtedly be angered to lose access to programming like NFL Football, “House” and “American Idol,” and some might cancel their subscriptions. At the same time, the Fox networks would lose 13 million viewers that its advertisers want to reach.

The companies will likely come to an agreement, however. Last year Time Warner Cable and Viacom (VIA), which owns MTV, Comedy Central and Nickelodeon, were deadlocked in a similar battle but reached an agreement early on Jan. 1